Question

Vasquez · Accepted Answer

To determine which function has a greater value when

x = 24

, we can substitute

x = 24

into each function and compare the resulting values.
a) The function of the line passing through A and B:
The equation of the line passing through points A(1,7) and B(-3,-9) can be found using the point-slope form:

y - y_{1} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \cdot (x - x_{1})

Substituting the coordinates of point A(1,7) and point B(-3,-9):

y - 7 = \frac{- 9 - 7}{- 3 - 1} \cdot (x - 1)

Simplifying:

y - 7 = \frac{- 16}{- 4} \cdot (x - 1)

y - 7 = 4 (x - 1)

y - 7 = 4 x - 4

y = 4 x + 3

Substituting

x = 24

into the equation, we get:

y = 4 (24) + 3

y = 96 + 3

y = 99

Therefore, the value of the function of the line passing through A and B when

x = 24

is 99.
b) The linear function

y = 2.5 x - 15

:
Substituting

x = 24

into the equation, we get:

y = 2.5 (24) - 15

y = 60 - 15

y = 45

Therefore, the value of the linear function

y = 2.5 x - 15

when

x = 24

is 45.
c) Neither, they have the same value at

x = 24

.
Comparing the values we found, we see that the function of the line passing through A and B has a greater value when

x = 24

(99), while the linear function

y = 2.5 x - 15

has a value of 45. Therefore, the correct answer is:
a) The function of the line passing through A and B.

Answered question

Answer & Explanation

New Questions in Geometry

Triangle J K L is shown. The length of J K is 13, the length of K L is 11, and the length of L J is 19.Law of cosines: a2 = b2 + c2 – 2bccos(A)

Find the measure of AngleJ, the smallest angle in a triangle with sides measuring 11, 13, and 19. Round to the nearest whole degree.

30°
34°
42°
47°

Answer & Explanation

New Questions in Geometry

Triangle J K L is shown. The length of J K is 13, the length of K L is 11, and the length of L J is 19.Law of cosines: a2 = b2 + c2 – 2bccos(A)Find the measure of AngleJ, the smallest angle in a triangle with sides measuring 11, 13, and 19. Round to the nearest whole degree.30°34°42°47°